Question

x-k is a factor of p(x) =3x^2+17x-20 find value of k
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Answer 1

$\large \bold \red{ \underline{ \underline{answer}}} \\ \large \bold \green{k = 1} \\ \large \bold \green{k = \frac{ - 20}{3} }$

Step-by-step explanation:

$\large \bold \red{ \underline{ \underline{to \: find \: value \: of \: k}}} \\\large\bold\green{ \underline{ \underline{given}}} \\ \large \bold{x - k \: is \: factor \: of \: 3 {x}^{2} + 17x - 20 } \\ \large \bold{x - k = 0} \\ \large \bold{x = k} \\ \large \bold{put \: x = k \: in \: equation \: } \\ \large \bold{3 {k}^{2} + 17k - 20 = 0 } \\ \large \bold{3 {k}^{2} + 20k - 3k - 20 = 0 } \\ \large \bold{k(3k + 20) - 1(3k +20) = 0 } \\ \large \bold{(k - 1)(3k + 20) = 0} \\ \large \bold \blue{ \underline{ \underline{k = 1 \: \: and \: \: k = \frac{ - 20}{3} = answer }}}$

Answer 2

QUESTION:

x-k is a factor of p(x) =3x^2+17x-20 find value of k

ANSWER:

As (x-k) is a factor of given polynomial x.

so,

$x - k = 0$

$\huge\orange {x = k}$

$\blue {[we \: put \: the \: value \: of \: x \: in \: p(x)]}$

now,

$p(k) = 3 {k}^{2} + 17 \times k - 20 \\ p(k) = 3 {k}^{2} + 17k - 20$

$p(k) = 3 {k}^{2} + 20k - 3k - 20 \\ p(k) = k(3k + 20) - 1(3k + 20) \\ p(k) = (k - 1)(3k + 20)$

hence;

$\huge\blue {(k - 1)(3k + 20) = 0}$

so,

$k - 1 = 0 \\ k = 1 \\ \\ or \\ 3k + 20 = 0 \\ 3k = - 20 \\ k = \frac{ - 20}{3}$

FINAL ANSWER:

$\huge\purple {k = 1 \: or \: \frac{ - 20}{3}}$